We have been experiencing this very same issue at one of our sites. Symptoms are identical, both the MX and Cisco switch are set to auto duplex/speed and the port will not come up. Plug a laptop into either the MX or the switch and the port comes straight up. Often then plugging the MX back to the switch and it will then work. Once up it will work without issue until the unit is powered down for maintenance. We also had a very similar experience where the port would not come up and then over a weekend after leaving the devices connected we found the port had come up.
As has been mentioned seemed to be some strange negotiation issue, we assume a bug but unsure if the bug sits on the MX or switch side.
We have a Meraki MX84 (ver. 15.44) and a Cisco C2960X (ver. 12.2(2)E8), out of interest what are you running in your environment?
We have yet to try fixing the port speeds/duplex on both sides or upgrading the switch IOS. The issue is once the port comes back up the device is then in use so we don't get the chance to troubleshoot.
Interested to hear if any others experience similar issues. @Meraki2 Any other reports you have seen of this on your side?